Epidemic spreading and aging in temporal networks with memory

Modeling and simulation on the spreading dynamics of public opinion information in temporal group networks

In the new media environment, the constantly emerging social platforms further expand the channels for the propagation of public opinion. Under the framework of complex network theory and faced the needs of management practice, modeling the spreading dynamics of public opinion in temporal group networks is of great significance for understanding its spreading law and improving the governance system of cyberspace and the development of network science. Through analyzing the changes of group networks topology and the spreading rules of public opinion, the spreading model of public opinion in temporal group networks was proposed by coupling the two dynamic processes, and the spreading thresholds of public opinion in static and temporal group networks were derived respectively. Then, the spreading characteristics of public opinion under different network topology, as well as the influence of important parameters on public opinion spreading process were discussed with the help of simulation experiments. The research results indicated that the propagation of public opinion in static and temporal group networks exhibits both similar trends and differentiated characteristics; compared with Spreader, the propagation of public opinion in temporal group networks is more sensitive to Ignorant's behavior; both groups' and netizens' active probability have significant influence on public opinion propagation, but netizens' affects more. Based on the relevant results, this paper proposed a series of countermeasures such as, grading social platforms, strengthening relationship management between them and introducing time management systems, so as to promote the formation of a good network ecosystem and the modernization of the national governance system.

Integrate-and-fire model of disease transmission

We create an epidemiological susceptible-infected-susceptible model of disease transmission using integrate-and-fire nodes on a network, allowing memory of previous interactions and infections. Agents in the network sum infectious matter from their nearest neighbors at every time step, until they exceed their infection threshold, at which point they "fire" and become infected for as long as the recovery time. The model has memory of previous interactions by tracking the amount of infectious matter carried by agents as well as just binary infected or susceptible states, and the model has memory of previous infections by modeling immunity as increasing the infection threshold after recovery. Creating a simulation of the model on networks with a power-law degree distribution and homogeneous agent parameters, we find a single strain version of the model matches well with the England COVID-19 case data, with a root-mean-squared error of 0.014%. A simulation of a multistrain version of the model (where there is cross-strain immunity) matches well with the influenza strain A and strain B case numbers in Canada, with a root-mean-squared error of 0.002% and 0.0012%, respectively, though due to the coupling in the model, both strains peak in phase. Since the dynamics of the model successfully capture real-life transmission dynamics, we test interventions to study their effect on case numbers, with both quarantining and social gathering restrictions lowering the peak. Since the model has memory, the stricter the intervention, the higher the secondary peak when the restriction is removed, showing that interventions change only the shape of the curves and not the overall number infected in the population.

Burstiness and information spreading in active particle systems

We construct a temporal network using the two-dimensional Vicsek model. The bursts of the interevent times for a specific pair of particles are investigated numerically. We found that, for different noise strengths, the distribution of the interevent times of a target edge follows a heavy tail, revealing the burstiness of the signals. To further characterize the nature of the burstiness, we calculate the burstiness parameters and the memory coefficients. The results show that, near the phase transition points of the Vicsek model, the burstiness parameters reach the minimum values for each density, indicating a relationship between the phase transition of the Vicsek model and the bursty nature of the signals. Furthermore, we investigate the spreading dynamics on our temporal network using a susceptible-infected model and observe a positive correlation between them.

Research on the co-evolution of temporal networks structure and public opinion propagation

Under the new media environment, social platforms, as the carrier of information propagation, have shown a drastic change in their form and structure, endowing public opinion with unique propagation characteristics. In view of this, considering the dynamic changes of online social network (OSN) structure, this article intends to analyse the spreading mechanism of public opinion in temporal networks and improve the applicability of public opinion governance strategies. Combing the changes of OSN topology with the classical susceptible–infected–recovered (SIR) dynamics model, we constructed a co-evolution model of temporal networks structure and public opinion propagation, and the propagation threshold of public opinion was derived with the help of Markov process. Then, the propagation characteristics of public opinion in temporal networks and their co-evolution process under different factors were discussed through simulation experiments. The results show that the propagation of public opinion in temporal networks has faster speed and wider scope compared with that in static networks; netizens’ social activity has a phased impact on the evolution process of public opinion and with its significant heterogeneity, the propagation of public opinion is gradually suppressed; compared with [Formula: see text], the evolution process of public opinion in temporal networks is more sensitive to the state change of public opinion [Formula: see text]. Our research can further enrich the theoretical research system of network science and information science and also provide a certain decision-making reference for the regulators to reasonably govern the propagation of public opinion in social platforms.

Interplay of simplicial awareness contagion and epidemic spreading on time-varying multiplex networks

There has been growing interest in exploring the dynamical interplay of epidemic spreading and awareness diffusion within the multiplex network framework. Recent studies have demonstrated that pairwise interactions are not enough to characterize social contagion processes, but the complex mechanisms of influence and reinforcement should be considered. Meanwhile, the physical social interaction of individuals is not static but time-varying. Therefore, we propose a novel sUAU-tSIS model to characterize the interplay of simplicial awareness contagion and epidemic spreading on time-varying multiplex networks, in which one layer with 2-simplicial complexes is considered the virtual information layer to address the complex contagion mechanisms in awareness diffusion and the other layer with time-varying and memory effects is treated as the physical contact layer to mimic the temporal interaction pattern among population. The microscopic Markov chain approach based theoretical analysis is developed, and the epidemic threshold is also derived. The experimental results show that our theoretical method is in good agreement with the Monte Carlo simulations. Specifically, we find that the synergistic reinforcement mechanism coming from the group interactions promotes the diffusion of awareness, leading to the suppression of the spreading of epidemics. Furthermore, our results illustrate that the contact capacity of individuals, activity heterogeneity, and memory strength also play important roles in the two dynamics; interestingly, a crossover phenomenon can be observed when investigating the effects of activity heterogeneity and memory strength.

Sideward contact tracing and the control of epidemics in large gatherings

Effective contact tracing is crucial to containing epidemic spreading without disrupting societal activities, especially during a pandemic. Large gatherings play a key role, potentially favouring superspreading events. However, the effects of tracing in large groups have not been fully assessed so far. We show that in addition to forward tracing, which reconstructs to whom the disease spreads, and backward tracing, which searches from whom the disease spreads, a third 'sideward' tracing is always present, when tracing gatherings. This is an indirect tracing that detects infected asymptomatic individuals, even if they have been neither directly infected by nor directly transmitted the infection to the index case. We analyse this effect in a model of epidemic spreading for SARS-CoV-2, within the framework of simplicial activity-driven temporal networks. We determine the contribution of the three tracing mechanisms to the suppression of epidemic spreading, showing that sideward tracing induces a non-monotonic behaviour in the tracing efficiency, as a function of the size of the gatherings. Based on our results, we suggest an optimal choice for the sizes of the gatherings to be traced and we test the strategy on an empirical dataset of gatherings on a university campus.

MODIT: MOtif DIscovery in Temporal Networks

Temporal networks are graphs where each edge is linked with a timestamp, denoting when an interaction between two nodes happens. According to the most recently proposed definitions of the problem, motif search in temporal networks consists in finding and counting all connected temporal graphs Q (called motifs) occurring in a larger temporal network T, such that matched target edges follow the same chronological order imposed by edges in Q. In the last few years, several algorithms have been proposed to solve motif search, but most of them are limited to very small or specific motifs due to the computational complexity of the problem. In this paper, we present MODIT (MOtif DIscovery in Temporal Networks), an algorithm for counting motifs of any size in temporal networks, inspired by a very recent algorithm for subgraph isomorphism in temporal networks, called TemporalRI. Experiments show that for big motifs (more than 3 nodes and 3 edges) MODIT can efficiently retrieve them in reasonable time (up to few hours) in many networks of medium and large size and outperforms state-of-the art algorithms.

An integrated simulation framework for the prevention and mitigation of pandemics caused by airborne pathogens

In this work, we developed an integrated simulation framework for pandemic prevention and mitigation of pandemics caused by airborne pathogens, incorporating three sub-models, namely the spatial model, the mobility model, and the propagation model, to create a realistic simulation environment for the evaluation of the effectiveness of different countermeasures on the epidemic dynamics. The spatial model converts images of real cities obtained from Google Maps into undirected weighted graphs that capture the spatial arrangement of the streets utilized next for the mobility of individuals. The mobility model implements a stochastic agent-based approach, developed to assign specific routes to individuals moving in the city, through the use of stochastic processes, utilizing the weights of the underlying graph to deploy shortest path algorithms. The propagation model implements both the epidemiological model and the physical substance of the transmission of an airborne pathogen (in our approach, we investigate the transmission parameters of SARS-CoV-2). The deployment of a set of countermeasures was investigated in reducing the spread of the pathogen, where, through a series of repetitive simulation experiments, we evaluated the effectiveness of each countermeasure in pandemic prevention.

Self-initiated behavioral change and disease resurgence on activity-driven networks

We consider a population that experienced a first wave of infections, interrupted by strong, top-down, governmental restrictions and did not develop a significant immunity to prevent a second wave (i.e., resurgence). As restrictions are lifted, individuals adapt their social behavior to minimize the risk of infection. We explore two scenarios. In the first, individuals reduce their overall social activity towards the rest of the population. In the second scenario, they maintain normal social activity within a small community of peers (i.e., social bubble) while reducing social interactions with the rest of the population. In both cases, we investigate possible correlations between social activity and behavior change, reflecting, for example, the social dimension of certain occupations. We model these scenarios considering a susceptible-infected-recovered epidemic model unfolding on activity-driven networks. Extensive analytical and numerical results show that (i) a minority of very active individuals not changing behavior may nullify the efforts of the large majority of the population and (ii) imperfect social bubbles of normal social activity may be less effective than an overall reduction of social interactions.

Stochastic sampling effects favor manual over digital contact tracing

Isolation of symptomatic individuals, tracing and testing of their nonsymptomatic contacts are fundamental strategies for mitigating the current COVID-19 pandemic. The breaking of contagion chains relies on two complementary strategies: manual reconstruction of contacts based on interviews and a digital (app-based) privacy-preserving contact tracing. We compare their effectiveness using model parameters tailored to describe SARS-CoV-2 diffusion within the activity-driven model, a general empirically validated framework for network dynamics. We show that, even for equal probability of tracing a contact, manual tracing robustly performs better than the digital protocol, also taking into account the intrinsic delay and limited scalability of the manual procedure. This result is explained in terms of the stochastic sampling occurring during the case-by-case manual reconstruction of contacts, contrasted with the intrinsically prearranged nature of digital tracing, determined by the decision to adopt the app or not by each individual. The better performance of manual tracing is enhanced by heterogeneity in agent behavior: superspreaders not adopting the app are completely invisible to digital contact tracing, while they can be easily traced manually, due to their multiple contacts. We show that this intrinsic difference makes the manual procedure dominant in realistic hybrid protocols.

Random walks in time-varying networks with memory

Random walks process on networks plays a fundamental role in understanding the importance of nodes and the similarity of them, which has been widely applied in PageRank, information retrieval, and community detection, etc. An individual's memory has been proved to be crucial to affect network evolution and dynamical processes unfolding on the network. In this work, we study the random-walk process on an extended activity-driven network model by taking account of an individual's memory. We analyze how an individual's memory affects random-walk process unfolding on the network when the timescales of the processes of the random walk and the network evolution are comparable. Under the constraints of long-time evolution, we derive analytical solutions for the distribution of walkers at the stationary state and the mean first-passage time of the random-walk process. We find that, compared with the memoryless activity-driven model, an individual's memory enhances the activity fluctuation and leads to the formation of small clusters of mutual contacts with high activity nodes, which reduces a node's capability of gathering walkers, especially for the nodes with large activity, and memory also delays the mean first-passage time. The results on real networks also support the theoretical analysis and numerical results with artificial networks.

Active and inactive quarantine in epidemic spreading on adaptive activity-driven networks

We consider an epidemic process on adaptive activity-driven temporal networks, with adaptive behavior modeled as a change in activity and attractiveness due to infection. By using a mean-field approach, we derive an analytical estimate of the epidemic threshold for susceptible-infected-susceptible (SIS) and susceptible-infected-recovered (SIR) epidemic models for a general adaptive strategy, which strongly depends on the correlations between activity and attractiveness in the susceptible and infected states. We focus on strong social distancing, implementing two types of quarantine inspired by recent real case studies: an active quarantine, in which the population compensates the loss of links rewiring the ineffective connections towards nonquarantining nodes, and an inactive quarantine, in which the links with quarantined nodes are not rewired. Both strategies feature the same epidemic threshold but they strongly differ in the dynamics of the active phase. We show that the active quarantine is extremely less effective in reducing the impact of the epidemic in the active phase compared to the inactive one and that in the SIR model a late adoption of measures requires inactive quarantine to reach containment.

Spreading of computer viruses on time-varying networks

Social networks are the prime channel for the spreading of computer viruses. Yet the study of their propagation neglects the temporal nature of social interactions and the heterogeneity of users' susceptibility. Here, we introduce a theoretical framework that captures both properties. We study two realistic types of viruses propagating on temporal networks featuring Q categories of susceptibility and derive analytically the invasion threshold. We found that the temporal coupling of categories might increase the fragility of the system to cyber threats. Our results show that networks' dynamics and their interplay with users' features are crucial for the spreading of computer viruses.